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Derivatives Introduction . Professor André Farber Solvay Business School Université Libre de Bruxelles. 1.Introduction. Outline of this session Course outline Derivatives Forward contracts Options contracts The derivatives markets Futures contracts. Reference:

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DerivativesIntroduction

Professor André Farber

Solvay Business School

Université Libre de Bruxelles


1.Introduction

  • Outline of this session

    • Course outline

    • Derivatives

    • Forward contracts

    • Options contracts

    • The derivatives markets

    • Futures contracts

Derivatives 01 Introduction


  • Reference:

    John HULL Options, Futures and Other Derivatives, Sixth edition, Pearson Prentice Hall 2006

    or

    John HULL Options, Futures and Other Derivatives, Fifth edition, Prentice Hall 2003

  • Copies of my slides will be available on my website: www.ulb.ac.be/cours/solvay/farber

  • Grades:

    • Cases: 30%

    • Final exam: 70%

Derivatives 01 Introduction


Course outline

Derivatives 01 Introduction


Derivatives

  • A derivative is an instrument whose value depends on the value of other more basic underlying variables

  • 2 main families:

    • Forward, Futures, Swaps

    • Options

  • = DERIVATIVE INSTRUMENTS

    • value depends on some underlying asset

  • Derivatives 01 Introduction


    Forward contract: Definition

    • Contract whereby parties are committed:

      • to buy (sell)

      • an underlying asset

      • at some future date (maturity)

      • at a delivery price (forward price) set in advance

    • The forward price for a contract is the delivery price that would be applicable to the contract if were negotiated today (i.e., it is the delivery price that would make the contract worth exactly zero)

    • The forward price may be different for contracts of different maturities

    • Buying forward = "LONG" position

    • Selling forward = "SHORT" position

    • When contract initiated: No cash flow

    • Obligation to transact

    Derivatives 01 Introduction


    Forward contract: example

    • Underlying asset: Gold

    • Spot price:$380 / troy ounce

    • Maturity:6-month

    • Size of contract:100 troy ounces (2,835 grams)

    • Forward price:$390 / troy ounce

    Profit/Loss at maturity

    Gain/Loss

    Gain/Loss

    Long

    Short

    ST

    ST

    390

    390

    Derivatives 01 Introduction


    Derivatives Markets

    • Exchange traded

      • Traditionally exchanges have used the open-outcry system, but increasingly they are switching to electronic trading

      • Contracts are standard there is virtually no credit risk

    • Over-the-counter (OTC)

      • A computer- and telephone-linked network of dealers at financial institutions, corporations, and fund managers

      • Contracts can be non-standard and there is some small amount of credit risk

    • Europe

      Eurex:http://www.eurexchange.com/

      Liffe: http://www.liffe.com

      Matif : http://www.matif.fr

    • United States

    • Chicago Board of Trade http: //www.cbot.com

    Derivatives 01 Introduction


    Evolution of global market

    Derivatives 01 Introduction


    Global Market Size

    Source: BIS Quarterly Review, June 2006 – www.bis.org

    Derivatives 01 Introduction


    Why use derivatives?

    • To hedge risks

    • To speculate (take a view on the future direction of the market)

    • To lock in an arbitrage profit

    • To change the nature of a liability

    • To change the nature of an investment without incurring the costs of selling one portfolio and buying another

    Derivatives 01 Introduction


    Forward contract: Cash flows

    • Notations

      STPrice of underlying asset at maturity

      Ft Forward price (delivery price) set at time t<T

      Initiation Maturity T

      Long 0 ST - Ft

      Short 0 Ft - ST

    • Initial cash flow = 0 :delivery price equals forward price.

    • Credit risk during the whole life of forward contract.

    Derivatives 01 Introduction


    Forward contract: Locking in the result before maturity

    • Enter a new forward contract in opposite direction.

    • Ex: at time t1 : long forward at forward price F1

    • At time t2 (<T): short forward at new forward price F2

    • Gain/loss at maturity :

    • (ST - F1) + (F2 - ST ) = F2 - F1 no remaining uncertainty

    Derivatives 01 Introduction


    Futures contract: Definition

    • Institutionalized forward contract with daily settlement of gains and losses

    • Forward contract

      • Buy  long

      • sell short

    • Standardized

      • Maturity, Face value of contract

    • Traded on an organized exchange

      • Clearing house

    • Daily settlement of gains and losses (Marked to market)

    Example: Gold futures

    Trading unit: 100 troy ounces (2,835 grams)

    July 3, 2002

    Derivatives 01 Introduction


    Futures: Daily settlement and the clearing house

    • In a forward contract:

      • Buyer and seller face each other during the life of the contract

      • Gains and losses are realized when the contract expires

      • Credit risk

        BUYER  SELLER

    • In a futures contract

      • Gains and losses are realized daily (Marking to market)

      • The clearinghouse garantees contract performance : steps in to take a position opposite each party

        BUYER  CH  SELLER

    Derivatives 01 Introduction


    Futures: Margin requirements

    • INITIAL MARGIN : deposit to put up in a margin account

    • MAINTENANCE MARGIN : minimum level of the margin account

    • MARKING TO MARKET : balance in margin account adjusted daily

    • Equivalent to writing a new futures contract every day at new futures price

    • (Remember how to close of position on a forward)

    • Note: timing of cash flows different

    Margin

    LONG(buyer)

    + Size x (Ft+1 -Ft)

    IM

    -Size x (Ft+1 -Ft)

    SHORT(seller)

    MM

    Time

    Derivatives 01 Introduction


    Valuing forward contracts: Key ideas

    • Two different ways to own a unit of the underlying asset at maturity:

      • 1.Buy spot (SPOT PRICE: S0) and borrow

        => Interest and inventory costs

      • 2. Buy forward (AT FORWARD PRICE F0)

    • VALUATION PRINCIPLE: NO ARBITRAGE

    • In perfect markets, no free lunch: the 2 methods should cost the same.

    You can think of a derivative as a mixture of its constituent underliers, much as a cake is a mixture of eggs, flour and milk in carefully specified proportions. The derivative’s model provide a recipe for the mixture, one whose ingredients’ quantity vary with time.Emanuel Derman, Market and models, Risk July 2001

    Derivatives 01 Introduction


    Discount factors and interest rates

    • Review: Present value of Ct

      • PV(Ct) = Ct× Discount factor

  • With annual compounding:

    • Discount factor = 1 / (1+r)t

  • With continuous compounding:

    • Discount factor = 1 / ert = e-rt

  • Derivatives 01 Introduction


    t = 0

    t = 1

    ST–F0

    0

    Should be equal

    -300

    + ST

    +300

    -315.38

    0

    ST-315.38

    Forward contract valuation : No income on underlying asset

    • Example: Gold (provides no income + no storage cost)

      • Current spot price S0 = $300/oz

      • Interest rate (with continuous compounding) r = 5%

      • Time until delivery (maturity of forward contract) T = 1

  • Forward price F0 ?

  • Strategy 1: buy forward

    Strategy 2: buy spot and borrow

    Buy spot

    Borrow

    Derivatives 01 Introduction


    Forward price and value of forward contract

    • Forward price:

    • Remember: the forward price is the delivery price which sets the value of a forward contract equal to zero.

    • Value of forward contract with delivery price K

    • You can check that f = 0 for K = S0er T

    Derivatives 01 Introduction


    Arbitrage

    • If F0 ≠ S0 e rT: arbitrage opportunity

    • Cash and carry arbitrage if: F0 > S0 e rT

      • Borrow S0, buy spot and sell forward at forward price F0

  • Reverse cash and carry arbitrage if S0 e rT > F0

    • Short asset, invest and buy forward at forward price F0

  • Derivatives 01 Introduction


    Arbitrage: examples

    • Gold – S0 = 300, r = 5%, T = 1S0erT = 315. 38

    • If forward price = 320

      • Buy spot-300+S1

      • Borrow+300-315.38

      • Sell forward0+320 – S1

      • Total0+ 4.62

  • If forward price = 310

    • Sell spot+300-S1

    • Invest-300+315.38

    • Buy forward0 S1 – 310

    • Total0+ 5.38

  • Derivatives 01 Introduction


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